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Sampled-data control and stability of sets for nonlinear systems. (English) Zbl 1207.93063

Summary: This paper is devoted to the investigation of the relation between stability properties of nonlinear closed-loop control systems and those of families of approximations with respect to a given set. Firstly, such relation is derived for continuous-time closed-loop systems and the associated sampled-data systems. Secondly, stability results are presented for parametrized families of exact and approximate discrete-time models considered with a parametrized family of feedbacks. In both cases, the sampling period is allowed to vary from step to step, and the stability is investigated with respect to nonempty closed (not necessarily compact) sets. Necessary and sufficient conditions are presented on the stability of approximations ensuring stability of the approximated systems.

MSC:

93C57 Sampled-data control/observation systems
93D15 Stabilization of systems by feedback
93C10 Nonlinear systems in control theory

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